Integrable order parameter dynamics of globally coupled oscillators

Pritula, G. M.; Prytula, Vladyslav; Usatenko, O. V.

doi:10.1088/1751-8113/49/6/065101

Cited by 3 publications

(2 citation statements)

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“…Now, it is straightforward to arrive at a class of macroscopic variables, corresponding to the higher orders, as the equations of motion of the centroid. Nevertheless, many macroscopic properties can be deduced even from the evolution equation of the macroscopic variables corresponding to the first order approximation [31,32]. However, we have also verified the emergence of similar results for the second order approximation in the current investigation.…”

Section: Mean-field Approximationsupporting

confidence: 82%

“…( 1), cannot be solved exactly. However, it can be reduced to a system of two evolution equations for the macroscopic order parameters, corresponding to the mean-field and the shape parameters, within the self-consistent field approach under the strong coupling limit [31,32]. To be specific, we adopt a mean-field approach proposed by Monte and Ovidio [31] under a narrow distribution of the Hopf bifurcation parameter and in the strong coupling limit, which is based on a moment expansion and a closure assumption [31].…”

Section: Mean-field Approximationmentioning

confidence: 99%

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Symmetry breaking induced tipping to aging

Gowthaman,

Chandrasekar,

Senthilkumar

et al. 2021

Preprint

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The competing effect of heterogeneity and symmetry breaking coupling on the emerging dynamics in a system of N globally coupled Stuart-Landau oscillators is investigated. Increasing the heterogeneity, using the standard deviation of the Hopf bifurcation parameter, favors the macroscopic oscillatory state for low values of the symmetry breaking coupling and inhomogeneous steady state for larger values of the coupling. There is also a transition, tipping, to homogeneous steady state (aging state) from the macroscopic oscillatory state. The limiting factor in the diffusive coupling favors the macroscopic oscillatory state even in the presence of a large fraction of inactive oscillators in the network thereby increasing the robustness of the network. The globally coupled oscillators are reduced to a system of two evolution equations for the macroscopic order parameters, corresponding to the mean-field and the shape parameter, using the self-consistent field approach. The bifurcation diagrams obtained from the mean-field variables elucidate various bifurcation scenarios responsible for the dynamical transitions observed in N globally coupled Stuart-Landau oscillators. In particular, tipping to the aging state is found to occur via the Hopf and pitchfork bifurcations illustrating the phenomenon of bifurcation induced tipping. Analytical stability (critical) curves of these bifurcations, deduced from the mean-field variables, are found to fairly well agree with the simulation results.

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Section: Mean-field Approximationsupporting

confidence: 82%